Adrian Kotelba

Adaptive Time Misalignment Compensation in Envelope Tracking Amplifiers

This paper considers the compensation of time misalignment between RF and envelope signals of envelope tracking (ET) amplifier. In particular, we propose methods to compensate the time misalignment and compare them to a previously presented method. Our simulation results indicate that the proposed methods give very accurate timing estimates. In the presence of optimal predistorter, we achieve with 90 percent probability adjacent channel power (ACP) level of -80 dB. With adaptive predistorters, we cannot see any degradation of ACP comparing to case of ideal timing. On the other hand, the proposed methods give roughly 10 dB better ACP than the previously presented method.

Relationship of Average Transmitted and Received Energies in Adaptive Transmission

This paper studies the analytical relationship between the average transmitted and received energies under several adaptive transmitter power control methods, including water filling, truncated power inversion, and downlink beamforming. The study is applicable to many fading channel scenarios, including frequency-nonselective, frequency-selective, and multiple-input-multiple-output (MIMO) channels. Both the average transmitted and received energies are commonly used in performance comparisons, and the selection depends on what one wants to investigate. The transmitted energy is known to be the basic system resource. In the case of adaptive transmission, the average transmitted energy should, in general, be used instead of the average received energy. The use of transmitted energy leads to the normalization problem of the channel. The ratio of received energy to transmitted energy is the energy gain of the channel. All physical systems follow an energy-conservation law, which implies that the energy gain of the channel is less than or equal to 1. The major approaches for normalization include the setting of either the average energy gain or the peak energy gain to unity. In the normalization, the average energy gain is defined for a signal whose energy is uniformly distributed across the frequency and spatial dimensions. The peak energy gain of many mathematical fading models is not bounded, and those models cannot be normalized by the peak energy gain. We show that the proper normalization of the mathematical model and the selection of the correct performance measure are of critical importance in comparative performance analysis of adaptive transmission systems.

Error Probability of Energy Detected Multilevel PAM Signals in Lognormal Multipath Fading Channels

Noncoherent multilevel systems have been typically analyzed with spectrally inefficient orthogonal modulation methods. In this paper, we present a novel error probability analysis of energy detected (ED) signals with spectrally efficient multilevel pulse amplitude modulation (PAM). One of the main challenges in the analysis of ED systems with the multilevel PAM is to find analytical methods to evaluate and optimize the performance of ED systems with respect to arbitrary system parameters, e.g., decision thresholds for chi-squared-distributed decision variables, integration time, bandwidth, and number of modulation levels. We propose analytically tractable methods that can be efficiently used to design spectrally efficient ED systems for short-range, wideband, and high data rate wireless communications in lognormal multipath fading channels with uncorrelated diversity paths.

Sensitivity of energy detected multilevel PAM systems to threshold mismatch

In this paper we theoretically evaluate the sensitivity resulted from a decision threshold mismatch with multilevel and energy detected pulse amplitude modulated (ED-PAM) signals. We quantify the relation between the threshold offset and the degradation in the required signal-to-noise ratio to preserve a desired symbol error rate. Based on the analysis we conclude some useful guidelines with respect to various system parameters. One of the main problems in an ED-PAM with arbitrary number of modulation levels, integration time, and bandwidth is to find a simple way to calculate the optimal threshold values. We rise to this challenge by proposing a new multilevel threshold calculation method which is attractive to use from both performance and complexity point of views for a wide range of system parameters. The results can be used, e.g., in an impulse radio for high data rate short-range wireless communications.

Energy detection of multilevel PAM signals with systematic threshold mismatch

We address a symbol decision problem with spectrally efficient energy detected multilevel pulse amplitude modulated (PAM) signals. First, we analytically quantify the relationship between a systematic threshold mismatch and the required increase of the average signal-to-noise ratio to preserve a desired symbol error rate. For the case in which such an increase is not tolerable, we present a novel near-optimal multilevel threshold selection scheme, which is accurate for a wide range of system parameters.

Adaptive Predistortion Architecture for Nonideal Radio Transmitter

A nonideal radio transmitter both distorts the desired signal and generates spectral regrowth causing interference to adjacent channels. Predistortion techniques can be used to minimize these effects. The joint effect of different types of nonidealities is not straightforward to analyze and has not yet been studied in detail in the literature. In this paper, we demonstrate how to adaptively predistort a nonlinear high power amplifier and an I/Q modulator, and to compensate the frequency response of a radio frequency filter. The study considers the spatial order of adaptive predistorters and the temporal sequence of adaptation steps. In this way, both the system capacity and the power efficiency are improved.

Full length article: Error performance of PAM systems using energy detection with optimal and suboptimal decision thresholds

In this paper, we consider the error probability for multilevel pulse amplitude modulated (PAM) signals, which are used with a multipath diversity combiner based on energy detection (ED). A distinctive feature of ED combined with nonconstant envelope signals is that the symbol decision thresholds need to be determined from a non-Gaussian distributed decision variable. We first present a novel theoretical analysis framework which provides a basis to predict the error performance of ED-PAM systems with optimal maximum likelihood decision thresholds in general multipath fading channels with arbitrary number of degrees of freedom. We then use frequency-selective lognormal fading channels as a case example and evaluate simple approximations for the error probability. Moreover, the analysis is extended to include the joint effect of systematic and random threshold deviation on the error probability with suboptimal but practical data-aided threshold estimation.

Nondata-Aided Hypothesis Testing of PAM Signals with Energy Detection

In this letter, we consider the problem of nondata-aided (NDA) detection of multilevel pulse-amplitude-modulated (PAM) signals combined with energy detection. We show that it is possible to estimate proper thresholds for the symbol decision without using redundant signals. Furthermore, we present an analytical method to evaluate the effect of pattern noise on the error performance of the NDA scheme with respect to the number of modulation levels and the convergence rate. With relatively low numbers of degrees of freedom and slow fading, which are typical for short-range systems using multiband modulation, the performance of the NDA scheme turns out to be asymptotically comparable to that of the optimal threshold selection.

Compensation of linear and nonlinear distortions in envelope tracking amplifier

This paper considers the compensation of linear and nonlinear distortions which are present in RF part of envelope tracking (ET) amplifier. In particular, we consider the compensation of magnitude and phase responses of analog filters, amplifier nonlinearity, and possible time misalignment between signals in RF and envelope branches. We propose a new adaptive predistorter architecture for ET amplifiers. Our analytical results indicate that the proposed architecture is a more general than the state-of-the-art architecture and is guaranteed to work with any ET amplifier. Furthermore, our simulations show that in order to keep adjacent channel power ratio below -60 dB, at least 9th order polynomial predistorter is needed. A comparable performance is obtained with look-up-table based predistorter having only 16 entries.

Compensation of time misalignment between input signals in envelope-tracking amplifiers

This paper considers a problem of time-misalignment between envelope and RF signals in envelope-tracking amplifiers. We propose two novel time-misalignment compensation methods which are based on the concepts of self-tuning control and model reference control from adaptive control theory. The performance of proposed methods, which we measure by the achievable adjacent-channel power ratio, is compared to the performance of the state-of-the-art method. Simulation results suggest that the time-misalignment compensation which is based on self-tuning structure offers a comparable performance as the state-of-the-art method. On the other hand, the time-misalignment compensation which is based on model reference structure outperforms the state-of-the-art method by 20 dB on the average. Furthermore, compensation with model reference structure appears to be very robust to changes in system parameters.